problem with my fixed/random effects method

[Anna Fischer]

Hi everyone!!!
My name is Anna,I'm pretty new to this forum so please excuse if I'm using any of the options wrong!
I have a question concerning my bachelor thesis.
I'm doing a panel regression with a dataset I made myself. After implementing the breuschpagan and the hausman test I thought I was good to go doing a Fixed Effects Method (as the hausman test showed me to do so) and I already finished all the robustness checks when I realised that one of my variables is timeinvarient and therefor not included in my model.
Now I am thinking of doing a random effects model instead which would make more sense in the theoretical sense as the timeinvarient variable that is excluded in the model is quite important. But on the other hand it would make less sense in the methodological way as RE is biased by time-constant unobserved heterogeneity – Since time-constant unobserved heterogeneity is ubiquitous in non-experimental social research, RE estimates generally will be biased.
What do you guys think is the better idea?

For some context: I am doing my research on the impact of parties (partisan theory) on the share of renewable energies in germany by federal state for the years 2002 to 2020.
My timeinvariant variable therefor is a meteorological variable concerning the wind speed per federal state which is - safe to say - quite important considering the fact that wind energy is one of the biggest renewable energy sources in germany. so neglecting that would be quite a big thing.

So should I do a random effects analysis instead which would that the variation across entities is assumed to be random and uncorrelated with the predictor or independent variables included in the model which theoretically doesn't make much sense.

Another option is also doing a fixed effects model and also a crosssectional data regression.

I would be very glad if someone of you guys could help me and give me some advice!

Thanks and have a lovely weekend!

[George Ford]

is the time invariant variable of key interest, or just a control?

mundlak regression will give you a coefficient if you really need it.

[Anna Fischer]

George Ford thanks for your reply! yes indeed it is just a control but i do find it quite important for my model and rather don't want to miss it in the model.
would you explain your idea of the mundlak regression to me? do i get it right, that this would mean that i do my normal fixed effects method but than after that do the mundlak regression with the group means of the independent variables and the controlvariables? thanks in advance!!

[Clyde Schechter]

it is just a control but i do find it quite important for my model and rather don't want to miss it in the model.

In the context of what was said in #1 this sentence verges on contradicting itself.

If it is there simply "as a control," that is, as a nuisance variable whose contribution to outcome variance must be adjusted for, then using a fixed effects model there is no need to include this one. The fixed effects, by themselves, adjust for ("control") all time-invariant attributes of the panel, both measured and unmeasured. So it is completely unnecessary to include this variable for that purpose.

If you mean that it is important in some other sense, that is, your research goals require you to estimate its between-panel effects (or, more exactly, how much the between panel effects differ from the within panel effects), then you can do that, as George Ford suggested, using the Mundlak model. If you are using Stata version 18.5, you can do that with the -xtreg, cre- command. If you have an earlier version of Stata, you can download -xthybrid- from SSC and use that for the purpose. Be sure to read the -xthybrid- helpfile before using the command so that you understand how to write the command and how to interpret the output.

[Carlo Lazzaro]

Anna:
as an aside to George and Clyde's excellent guidance, I have some comments on other issues concerning your post:
1) if -fe- is the way to go and you go -re-, -re- is inconsistent. Therefore, your coefficients are unreliable. Mundlak is a possible fix, but the panel should be balanced (however, see also Correlated random effects models with unbalanced panels - ScienceDirect);
2) are you sure that the wind speed for federal state is a time-invariant predictor?
3) I would not sponsor "a fixed effects model and also a crosssectional data regression".

[Anna Fischer]

Carlo Lazzaro thank you for your reply, I am going to answer your bullet points one by one.

1) I thought that you could indeed make exceptions and not follow the Hausman Test if it makes sense in your theoretical argumentation - is that not the case?
What I am finding online about the Mundlak regression implies that it is only done in the context of a random regression but not of a fixed regression. Did I get that wrong? And am I right thinking that I would just do my normal regressions (xtreg all the variables, fe) and AFTER THAT do Mundlak regressions?

2) I created the Data Set myself not having access to that many geographical soources so I created the variable of the wind speed from a website called "Windatlas" that only has their values as a mean for a specific time frame. That is why I do only have one average value for each federal state which I will apply for all the years I am analyzing.

3) Why is that? I would do that as a step BEFORE I do the Panelanalysis with my fixed effects model.

Thank you again, your feedback was very interesting and helpful!

Kind regards,
Anna
(Stata 18.0 I think)

[Jeff Wooldridge]

Anna: Do you have a balanced panel? Same years (without any missing data)? If so, it is easy to do the Mundlak estimation and confirm it is accurate identical to FE on the time-varying variables. Plus, you get a coefficient on time-invariant variables. Plus you get a robust version of the Hausman test if you use vce(robust) or vce(cluster id). In short, it does everything FE does and more.

About the usage of the H test: the default is typically to use FE (equivalently, Mundlak) with your kind of data structure. The H test often has poor power, so you shouldn’t automatically use RE if the Mundlak version of the H test doesn’t reject. If FE gives precise enough estimates, go with that. Mundlak is the same and gives coefficients on the time-invariant controls.

[Carlo Lazzaro]

Anna:
1) yes, you can ignore the indication of -hausman. test, but see Analysis of Panel Data (cambridge.org) page 47-48;56-58:
2) thanks for clarifying;
3) the -fe- estimator focuses on the within-panel variation, whereas the (pooled) OLS estimator on a mix between the within and between variations; in addition, in (pooled OLS) you should impose the -vce(cluster panelid)- standard errors, as your observations belonging to the same panel are not independent. If you want to compare to estimators applied to panel data, it probably makes more sense to go -fe- and -re- (with the caveat that, if -fe- is the way to go, -re- is inconsistent);
4) strategic (and unsolicited) advice: whatever your research approach is, discuss every single step with your supervisor, to avoid unexpected going-arounds when the runway is in sight !